The gcj mailing-list (and, more specifically, Ranjit Mathew, the author of the scripts I used to build a Win32 gcj) helped me; I'm not sure I liked the answer, though...

So I need to build an SWT DLL using a specific flag (-fno-omit-frame-pointer). Otherwise, the unwinding code (whatever kind of stack-walking thingy that may be) get confused.

I've actually been able to build a working DLL, but I had to use the standard Windows toolchain (which, surprisingly to me, I could download for free). Adapting those makefiles to gcj will be an interesting exercise...

I'd never thought my desire to integrate open source java software to Windows would lead me to the installation and fiddling with of so much Microsoft tools...